text: /****************************************************************************
   * libs/libc/stdio/lib_dtoa.c
   *
   * This file was ported to NuttX by Yolande Cates.
   *
   * Copyright (c) 1990, 1993
   *      The Regents of the University of California.  All rights reserved.
   *
   * This code is derived from software contributed to Berkeley by
   * Chris Torek.
   *
   * Redistribution and use in source and binary forms, with or without
   * modification, are permitted provided that the following conditions
   * are met:
   * 1. Redistributions of source code must retain the above copyright
   *    notice, this list of conditions and the following disclaimer.
   * 2. Redistributions in binary form must reproduce the above copyright
   *    notice, this list of conditions and the following disclaimer in the
   *    documentation and/or other materials provided with the distribution.
   * 3. All advertising materials mentioning features or use of this software
   *    must display the following acknowledgement:
   *      This product includes software developed by the University of
   *      California, Berkeley and its contributors.
   * 4. Neither the name of the University nor the names of its contributors
   *    may be used to endorse or promote products derived from this software
   *    without specific prior written permission.
   *
   * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
   * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
   * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
   * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
   * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
   * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
   * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
   * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
   * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
   * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
   * SUCH DAMAGE.
   *
   ****************************************************************************/
  
  /****************************************************************************
   * Included Files
   ****************************************************************************/
  
  #include <nuttx/config.h>
  
  #include <stdint.h>
  #include <string.h>
  
  #include "libc.h"
  
  /****************************************************************************
   * Pre-processor Definitions
   ****************************************************************************/
  
  #ifdef Unsigned_Shifts
  #  define Sign_Extend(a,b) if (b < 0) a |= 0xffff0000;
  #else
  #  define Sign_Extend(a,b)      /* no-op */
  #endif
  
  #ifdef CONFIG_ENDIAN_BIG
  #  define word0(x) ((uint32_t *)&x)[0]
  #  define word1(x) ((uint32_t *)&x)[1]
  #else
  #  define word0(x) ((uint32_t *)&x)[1]
  #  define word1(x) ((uint32_t *)&x)[0]
  #endif
  
  #ifdef CONFIG_ENDIAN_BIG
  #  define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \
                           ((unsigned short *)a)[1] = (unsigned short)c, a++)
  #else
  #  define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \
                           ((unsigned short *)a)[0] = (unsigned short)c, a++)
  #endif
  
  #define Exp_shift  20
  #define Exp_shift1 20
  #define Exp_msk1    0x100000
  #define Exp_msk11   0x100000
  #define Exp_mask  0x7ff00000
  #define P 53
  #define Bias 1023
  #define IEEE_Arith
  #define Emin (-1022)
  #define Exp_1  0x3ff00000
  #define Exp_11 0x3ff00000
  #define Ebits 11
  #define Frac_mask  0xfffff
  #define Frac_mask1 0xfffff
  #define Ten_pmax 22
  #define Bletch 0x10
  #define Bndry_mask  0xfffff
  #define Bndry_mask1 0xfffff
  #define LSB 1
  #define Sign_bit 0x80000000
  #define Log2P 1
  #define Tiny0 0
  #define Tiny1 1
  #define Quick_max 14
  #define Int_max 14
  #define Infinite(x) (word0(x) == 0x7ff00000)    /* sufficient test for here */
  
  #define Kmax 15
  
  #define Bcopy(x,y) memcpy((char *)&x->sign, (char *)&y->sign, \
                            y->wds*sizeof(long) + 2*sizeof(int))
  
  /****************************************************************************
   * Private Type Definitions
   ****************************************************************************/
  
  struct Bigint
  {
    struct Bigint *next;
    int k, maxwds, sign, wds;
    unsigned long x[1];
  };
  
  typedef struct Bigint Bigint;
  
  /****************************************************************************
   * Private Data
   ****************************************************************************/
  
  static Bigint *freelist[Kmax + 1];
  
  /****************************************************************************
   * Private Functions
   ****************************************************************************/
  
  static Bigint *Balloc(int k)
  {
    int x;
    Bigint *rv;
  
    if ((rv = freelist[k]))
      {
        freelist[k] = rv->next;
      }
    else
      {
        x = 1 << k;
        rv = (Bigint *)lib_malloc(sizeof(Bigint) + (x - 1) * sizeof(long));
        rv->k = k;
        rv->maxwds = x;
      }
  
    rv->sign = rv->wds = 0;
    return rv;
  }
  
  static void Bfree(Bigint * v)
  {
    if (v)
      {
        v->next = freelist[v->k];
        freelist[v->k] = v;
      }
  }
  
  /* multiply by m and add a */
  
  static Bigint *multadd(Bigint * b, int m, int a)
  {
    int i, wds;
    unsigned long *x, y;
  #ifdef Pack_32
    unsigned long xi, z;
  #endif
    Bigint *b1;
  
    wds = b->wds;
    x = b->x;
    i = 0;
    do
      {
  #ifdef Pack_32
        xi = *x;
        y = (xi & 0xffff) * m + a;
        z = (xi >> 16) * m + (y >> 16);
        a = (int)(z >> 16);
        *x++ = (z << 16) + (y & 0xffff);
  #else
        y = *x * m + a;
        a = (int)(y >> 16);
        *x++ = y & 0xffff;
  #endif
      }
    while (++i < wds);
  
    if (a)
      {
        if (wds >= b->maxwds)
          {
            b1 = Balloc(b->k + 1);
            Bcopy(b1, b);
            Bfree(b);
            b = b1;
          }
        b->x[wds++] = a;
        b->wds = wds;
      }
  
    return b;
  }
  
  static int hi0bits(unsigned long x)
  {
    int k = 0;
  
    if (!(x & 0xffff0000))
      {
        k = 16;
        x <<= 16;
      }
  
    if (!(x & 0xff000000))
      {
        k += 8;
        x <<= 8;
      }
  
    if (!(x & 0xf0000000))
      {
        k += 4;
        x <<= 4;
      }
  
    if (!(x & 0xc0000000))
      {
        k += 2;
        x <<= 2;
      }
  
    if (!(x & 0x80000000))
      {
        k++;
        if (!(x & 0x40000000))
          {
            return 32;
          }
      }
  
    return k;
  }
  
  static int lo0bits(unsigned long *y)
  {
    int k;
    unsigned long x = *y;
  
    if (x & 7)
      {
        if (x & 1)
          {
            return 0;
          }
  
        if (x & 2)
          {
            *y = x >> 1;
            return 1;
          }
  
        *y = x >> 2;
        return 2;
      }
  
    k = 0;
    if (!(x & 0xffff))
      {
        k = 16;
        x >>= 16;
      }
  
    if (!(x & 0xff))
      {
        k += 8;
        x >>= 8;
      }
  
    if (!(x & 0xf))
      {
        k += 4;
        x >>= 4;
      }
  
    if (!(x & 0x3))
      {
        k += 2;
        x >>= 2;
      }
  
    if (!(x & 1))
      {
        k++;
        x >>= 1;
        if (!x & 1)
          {
            return 32;
          }
      }
  
    *y = x;
    return k;
  }
  
  static Bigint *i2b(int i)
  {
    Bigint *b;
  
    b = Balloc(1);
    b->x[0] = i;
    b->wds = 1;
    return b;
  }
  
  static Bigint *mult(Bigint * a, Bigint * b)
  {
    Bigint *c;
    int k, wa, wb, wc;
    unsigned long carry, y, z;
    unsigned long *x, *xa, *xae, *xb, *xbe, *xc, *xc0;
  #ifdef Pack_32
    uint32_t z2;
  #endif
  
    if (a->wds < b->wds)
      {
        c = a;
        a = b;
        b = c;
      }
  
    k = a->k;
    wa = a->wds;
    wb = b->wds;
    wc = wa + wb;
    if (wc > a->maxwds)
      {
        k++;
      }
  
    c = Balloc(k);
    for (x = c->x, xa = x + wc; x < xa; x++)
      {
        *x = 0;
      }
  
    xa = a->x;
    xae = xa + wa;
    xb = b->x;
    xbe = xb + wb;
    xc0 = c->x;
  #ifdef Pack_32
    for (; xb < xbe; xb++, xc0++)
      {
        if ((y = *xb & 0xffff))
          {
            x = xa;
            xc = xc0;
            carry = 0;
            do
              {
                z = (*x & 0xffff) * y + (*xc & 0xffff) + carry;
                carry = z >> 16;
                z2 = (*x++ >> 16) * y + (*xc >> 16) + carry;
                carry = z2 >> 16;
                Storeinc(xc, z2, z);
              }
            while (x < xae);
  
            *xc = carry;
          }
  
        if ((y = *xb >> 16))
          {
            x = xa;
            xc = xc0;
            carry = 0;
            z2 = *xc;
            do
              {
                z = (*x & 0xffff) * y + (*xc >> 16) + carry;
                carry = z >> 16;
                Storeinc(xc, z, z2);
                z2 = (*x++ >> 16) * y + (*xc & 0xffff) + carry;
                carry = z2 >> 16;
              }
            while (x < xae);
  
            *xc = z2;
          }
      }
  #else
    for (; xb < xbe; xc0++)
      {
        if ((y = *xb++))
          {
            x = xa;
            xc = xc0;
            carry = 0;
            do
              {
                z = *x++ * y + *xc + carry;
                carry = z >> 16;
                *xc++ = z & 0xffff;
              }
            while (x < xae);
  
            *xc = carry;
          }
      }
  #endif
  
    for (xc0 = c->x, xc = xc0 + wc; wc > 0 && !*--xc; --wc);
    c->wds = wc;
    return c;
  }
  
  static Bigint *p5s;
  
  static Bigint *pow5mult(Bigint * b, int k)
  {
    Bigint *b1, *p5, *p51;
    int i;
    static int p05[3] =
    {
      5, 25, 125
    };
  
    if ((i = k & 3))
      b = multadd(b, p05[i - 1], 0);
  
    if (!(k >>= 2))
      {
        return b;
      }
  
    if (!(p5 = p5s))
      {
        /* first time */
        p5 = p5s = i2b(625);
        p5->next = 0;
      }
  
    for (; ; )
      {
        if (k & 1)
          {
            b1 = mult(b, p5);
            Bfree(b);
            b = b1;
          }
  
        if (!(k >>= 1))
          {
            break;
          }
  
        if (!(p51 = p5->next))
          {
            p51 = p5->next = mult(p5, p5);
            p51->next = 0;
          }
  
        p5 = p51;
      }
  
    return b;
  }
  
  static Bigint *lshift(Bigint * b, int k)
  {
    int i, k1, n, n1;
    Bigint *b1;
    unsigned long *x, *x1, *xe, z;
  
  #ifdef Pack_32
    n = k >> 5;
  #else
    n = k >> 4;
  #endif
    k1 = b->k;
    n1 = n + b->wds + 1;
    for (i = b->maxwds; n1 > i; i <<= 1)
      {
        k1++;
      }
  
    b1 = Balloc(k1);
    x1 = b1->x;
    for (i = 0; i < n; i++)
      {
        *x1++ = 0;
      }
  
    x = b->x;
    xe = x + b->wds;
  #ifdef Pack_32
    if (k &= 0x1f)
      {
        k1 = 32 - k;
        z = 0;
        do
          {
            *x1++ = *x << k | z;
            z = *x++ >> k1;
          }
        while (x < xe);
  
        if ((*x1 = z))
          {
            ++n1;
          }
      }
  #else
    if (k &= 0xf)
      {
        k1 = 16 - k;
        z = 0;
        do
          {
            *x1++ = ((*x << k) & 0xffff) | z;
            z = *x++ >> k1;
          }
        while (x < xe);
  
        if ((*x1 = z))
          {
            ++n1;
          }
      }
  #endif
    else
      {
        do
          {
            *x1++ = *x++;
          }
        while (x < xe);
      }
  
    b1->wds = n1 - 1;
    Bfree(b);
    return b1;
  }
  
  static int cmp(Bigint * a, Bigint * b)
  {
    unsigned long *xa, *xa0, *xb, *xb0;
    int i, j;
  
    i = a->wds;
    j = b->wds;
  
  #ifdef CONFIG_DEBUG_LIB
    if (i > 1 && !a->x[i - 1])
     {
      lerr("ERROR: cmp called with a->x[a->wds-1] == 0\n");
     }
  
    if (j > 1 && !b->x[j - 1])
     {
      lerr("ERROR: cmp called with b->x[b->wds-1] == 0\n");
     }
  #endif
  
    if (i -= j)
      {
        return i;
      }
  
    xa0 = a->x;
    xa = xa0 + j;
    xb0 = b->x;
    xb = xb0 + j;
  
    for (; ; )
      {
        if (*--xa != *--xb)
          {
            return *xa < *xb ? -1 : 1;
          }
  
        if (xa <= xa0)
          {
            break;
          }
      }
  
    return 0;
  }
  
  static Bigint *diff(Bigint * a, Bigint * b)
  {
    Bigint *c;
    int i, wa, wb;
    long borrow, y;               /* We need signed shifts here. */
    unsigned long *xa, *xae, *xb, *xbe, *xc;
  #ifdef Pack_32
    int32_t z;
  #endif
  
    i = cmp(a, b);
    if (!i)
      {
        c = Balloc(0);
        c->wds = 1;
        c->x[0] = 0;
        return c;
      }
  
    if (i < 0)
      {
        c = a;
        a = b;
        b = c;
        i = 1;
      }
    else
      {
        i = 0;
      }
  
    c = Balloc(a->k);
    c->sign = i;
    wa = a->wds;
    xa = a->x;
    xae = xa + wa;
    wb = b->wds;
    xb = b->x;
    xbe = xb + wb;
    xc = c->x;
    borrow = 0;
  #ifdef Pack_32
    do
      {
        y = (*xa & 0xffff) - (*xb & 0xffff) + borrow;
        borrow = y >> 16;
        Sign_Extend(borrow, y);
        z = (*xa++ >> 16) - (*xb++ >> 16) + borrow;
        borrow = z >> 16;
        Sign_Extend(borrow, z);
        Storeinc(xc, z, y);
      }
    while (xb < xbe);
  
    while (xa < xae)
      {
        y = (*xa & 0xffff) + borrow;
        borrow = y >> 16;
        Sign_Extend(borrow, y);
        z = (*xa++ >> 16) + borrow;
        borrow = z >> 16;
        Sign_Extend(borrow, z);
        Storeinc(xc, z, y);
      }
  #else
    do
      {
        y = *xa++ - *xb++ + borrow;
        borrow = y >> 16;
        Sign_Extend(borrow, y);
        *xc++ = y & 0xffff;
      }
    while (xb < xbe);
  
    while (xa < xae)
      {
        y = *xa++ + borrow;
        borrow = y >> 16;
        Sign_Extend(borrow, y);
        *xc++ = y & 0xffff;
      }
  #endif
  
    while (!*--xc)
      {
        wa--;
      }
  
    c->wds = wa;
    return c;
  }
  
  static Bigint *d2b(double d, int *e, int *bits)
  {
    Bigint *b;
    int de, i, k;
    unsigned long *x, y, z;
  
  #ifdef Pack_32
    b = Balloc(1);
  #else
    b = Balloc(2);
  #endif
    x = b->x;
  
    z = word0(d) & Frac_mask;
    word0(d) &= 0x7fffffff;       /* clear sign bit, which we ignore */
    if ((de = (int)(word0(d) >> Exp_shift)))
      z |= Exp_msk1;
  #ifdef Pack_32
    if ((y = word1(d)))
      {
        if ((k = lo0bits(&y)))
          {
            x[0] = y | z << (32 - k);
            z >>= k;
          }
        else
          {
            x[0] = y;
          }
  
        i = b->wds = (x[1] = z) ? 2 : 1;
      }
    else
      {
  #ifdef CONFIG_DEBUG_LIB
        if (!z)
          {
            lerr("ERROR: Zero passed to d2b\n");
          }
  #endif
        k = lo0bits(&z);
        x[0] = z;
        i = b->wds = 1;
        k += 32;
      }
  #else
    if ((y = word1(d)))
      {
        if ((k = lo0bits(&y)))
          if (k >= 16)
            {
              x[0] = y | ((z << (32 - k)) & 0xffff);
              x[1] = z >> (k - 16) & 0xffff;
              x[2] = z >> k;
              i = 2;
            }
          else
            {
              x[0] = y & 0xffff;
              x[1] = (y >> 16) | ((z << (16 - k)) & 0xffff);
              x[2] = z >> k & 0xffff;
              x[3] = z >> (k + 16);
              i = 3;
            }
        else
          {
            x[0] = y & 0xffff;
            x[1] = y >> 16;
            x[2] = z & 0xffff;
            x[3] = z >> 16;
            i = 3;
          }
      }
    else
      {
  #ifdef CONFIG_DEBUG_LIB
        if (!z)
          {
            lerr("ERROR: Zero passed to d2b\n");
          }
  #endif
        k = lo0bits(&z);
        if (k >= 16)
          {
            x[0] = z;
            i = 0;
          }
        else
          {
            x[0] = z & 0xffff;
            x[1] = z >> 16;
            i = 1;
          }
  
        k += 32;
      }
    while (!x[i])
      --i;
  
    b->wds = i + 1;
  #endif
    if (de)
      {
        *e = de - Bias - (P - 1) + k;
        *bits = P - k;
      }
    else
      {
        *e = de - Bias - (P - 1) + 1 + k;
  #ifdef Pack_32
        *bits = 32 * i - hi0bits(x[i - 1]);
  #else
        *bits = (i + 2) * 16 - hi0bits(x[i]);
  #endif
      }
  
    return b;
  }
  
  static const double tens[] =
  {
    1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
    1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
    1e20, 1e21, 1e22
  };
  
  #ifdef IEEE_Arith
  static const double bigtens[] =
  {
    1e16, 1e32, 1e64, 1e128, 1e256
  };
  
  #  define n_bigtens 5
  #else
  static const double bigtens[] =
  {
    1e16, 1e32
  };
  
  #  define n_bigtens 2
  #endif
  
  static int quorem(Bigint * b, Bigint * S)
  {
    int n;
    long borrow, y;
    unsigned long carry, q, ys;
    unsigned long *bx, *bxe, *sx, *sxe;
  #ifdef Pack_32
    int32_t z;
    uint32_t si, zs;
  #endif
  
    n = S->wds;
  
  #ifdef CONFIG_DEBUG_LIB
    if (b->wds > n)
      {
        lerr("ERROR: oversize b in quorem\n");
      }
  #endif
  
    if (b->wds < n)
      {
        return 0;
      }
  
    sx = S->x;
    sxe = sx + --n;
    bx = b->x;
    bxe = bx + n;
    q = *bxe / (*sxe + 1);        /* ensure q <= true quotient */
  
  #ifdef CONFIG_DEBUG_LIB
    if (q > 9)
      {
        lerr("ERROR: oversized quotient in quorem\n");
      }
  #endif
  
    if (q)
      {
        borrow = 0;
        carry = 0;
  
        do
          {
  #ifdef Pack_32
            si = *sx++;
            ys = (si & 0xffff) * q + carry;
            zs = (si >> 16) * q + (ys >> 16);
            carry = zs >> 16;
            y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
            borrow = y >> 16;
            Sign_Extend(borrow, y);
            z = (*bx >> 16) - (zs & 0xffff) + borrow;
            borrow = z >> 16;
            Sign_Extend(borrow, z);
            Storeinc(bx, z, y);
  #else
            ys = *sx++ * q + carry;
            carry = ys >> 16;
            y = *bx - (ys & 0xffff) + borrow;
            borrow = y >> 16;
            Sign_Extend(borrow, y);
            *bx++ = y & 0xffff;
  #endif
          }
        while (sx <= sxe);
  
        if (!*bxe)
          {
            bx = b->x;
            while (--bxe > bx && !*bxe)
              {
                --n;
              }
  
            b->wds = n;
          }
      }
  
    if (cmp(b, S) >= 0)
      {
        q++;
        borrow = 0;
        carry = 0;
        bx = b->x;
        sx = S->x;
  
        do
          {
  #ifdef Pack_32
            si = *sx++;
            ys = (si & 0xffff) + carry;
            zs = (si >> 16) + (ys >> 16);
            carry = zs >> 16;
            y = (*bx & 0xffff) - (ys & 0xffff) + borrow;
            borrow = y >> 16;
            Sign_Extend(borrow, y);
            z = (*bx >> 16) - (zs & 0xffff) + borrow;
            borrow = z >> 16;
            Sign_Extend(borrow, z);
            Storeinc(bx, z, y);
  #else
            ys = *sx++ + carry;
            carry = ys >> 16;
            y = *bx - (ys & 0xffff) + borrow;
            borrow = y >> 16;
            Sign_Extend(borrow, y);
            *bx++ = y & 0xffff;
  #endif
          }
        while (sx <= sxe);
  
        bx = b->x;
        bxe = bx + n;
        if (!*bxe)
          {
            while (--bxe > bx && !*bxe)
              --n;
  
            b->wds = n;
          }
      }
  
    return q;
  }
  
  /****************************************************************************
   * Public Functions
   ****************************************************************************/
  
  /* dtoa for IEEE arithmetic (dmg): convert double to ASCII string.
   *
   * Inspired by "How to Print Floating-Point Numbers Accurately" by
   * Guy L. Steele, Jr. and Jon L. White [Proc. ACM SIGPLAN '90, pp. 92-101].
   *
   * Modifications:
   *      1. Rather than iterating, we use a simple numeric overestimate
   *         to determine k = floor(log10(d)).  We scale relevant
   *         quantities using O(log2(k)) rather than O(k) multiplications.
   *      2. For some modes > 2 (corresponding to ecvt and fcvt), we don't
   *         try to generate digits strictly left to right.  Instead, we
   *         compute with fewer bits and propagate the carry if necessary
   *         when rounding the final digit up.  This is often faster.
   *      3. Under the assumption that input will be rounded nearest,
   *         mode 0 renders 1e23 as 1e23 rather than 9.999999999999999e22.
   *         That is, we allow equality in stopping tests when the
   *         round-nearest rule will give the same floating-point value
   *         as would satisfaction of the stopping test with strict
   *         inequality.
   *      4. We remove common factors of powers of 2 from relevant
   *         quantities.
   *      5. When converting floating-point integers less than 1e16,
   *         we use floating-point arithmetic rather than resorting
   *         to multiple-precision integers.
   *      6. When asked to produce fewer than 15 digits, we first try
   *         to get by with floating-point arithmetic; we resort to
   *         multiple-precision integer arithmetic only if we cannot
   *         guarantee that the floating-point calculation has given
   *         the correctly rounded result.  For k requested digits and
   *         "uniformly" distributed input, the probability is
   *         something like 10^(k-15) that we must resort to the int32_t
   *         calculation.
   */
  
  char *__dtoa(double d, int mode, int ndigits, int *decpt, int *sign, char **rve)
  {
    /* Arguments ndigits, decpt, sign are similar to those of ecvt and fcvt;
     * trailing zeros are suppressed from the returned string.  If not null, *rve
     * is set to point to the end of the return value.  If d is +-Infinity or
     * NaN, then *decpt is set to 9999.
     *
     * mode: 0 ==> shortest string that yields d when read in and rounded to
     * nearest. 1 ==> like 0, but with Steele & White stopping rule; e.g. with
     * IEEE P754 arithmetic , mode 0 gives 1e23 whereas mode 1 gives
     * 9.999999999999999e22. 2 ==> max(1,ndigits) significant digits.  This gives
     * a return value similar to that of ecvt, except that trailing zeros are
     * suppressed. 3 ==> through ndigits past the decimal point.  This gives a
     * return value similar to that from fcvt, except that trailing zeros are
     * suppressed, and ndigits can be negative. 4-9 should give the same return
     * values as 2-3, i.e., 4 <= mode <= 9 ==> same return as mode 2 + (mode &
     * 1).  These modes are mainly for debugging; often they run slower but
     * sometimes faster than modes 2-3. 4,5,8,9 ==> left-to-right digit
     * generation. 6-9 ==> don't try fast floating-point estimate (if
     * applicable).
     *
     * Values of mode other than 0-9 are treated as mode 0.
     *
     * Sufficient space is allocated to the return value to hold the suppressed
     * trailing zeros. */
  
    int bbits, b2, b5, be, dig, i, ieps, ilim = 0, ilim0, ilim1 = 0,
      j, j_1, k, k0, k_check, leftright, m2, m5, s2, s5, spec_case = 0, try_quick;
    long L;
    int denorm;
    unsigned long x;
    Bigint *b, *b1, *delta, *mlo = NULL, *mhi, *S;
    double d2, ds, eps;
    char *s, *s0;
    static Bigint *result;
    static int result_k;
  
    if (result)
      {
        result->k = result_k;
        result->maxwds = 1 << result_k;
        Bfree(result);
        result = 0;
      }
  
    if (word0(d) & Sign_bit)
      {
        /* Set sign for everything, including 0's and NaNs */
  
        *sign = 1;
        word0(d) &= ~Sign_bit;    /* clear sign bit */
      }
    else
      {
        *sign = 0;
      }
  
  #if defined(IEEE_Arith)
  #  ifdef IEEE_Arith
    if ((word0(d) & Exp_mask) == Exp_mask)
  #else
    if (word0(d) == 0x8000)
  #endif
      {
        /* Infinity or NaN */
  
        *decpt = 9999;
        s =
  #ifdef IEEE_Arith
          !word1(d) && !(word0(d) & 0xfffff) ? "Infinity" :
  #endif
          "NaN";
        if (rve)
          {
            *rve =
  #ifdef IEEE_Arith
              s[3] ? s + 8 :
  #endif
              s + 3;
          }
  
        return s;
      }
  #endif
  
    if (!d)
      {
        *decpt = 1;
        s = "0";
        if (rve)
          {
            *rve = s + 1;
          }
  
        return s;
      }
  
    b = d2b(d, &be, &bbits);
    if ((i = (int)(word0(d) >> Exp_shift1 & (Exp_mask >> Exp_shift1))))
      {
        d2 = d;
        word0(d2) &= Frac_mask1;
        word0(d2) |= Exp_11;
  
        /* log(x) ~=~ log(1.5) + (x-1.5)/1.5 log10(x) = log(x) / log(10) ~=~
         * log(1.5)/log(10) + (x-1.5)/(1.5*log(10)) log10(d) =
         * (i-Bias)*log(2)/log(10) + log10(d2) This suggests computing an
         * approximation k to log10(d) by k = (i - Bias)*0.301029995663981 + (
         * (d2-1.5)*0.289529654602168 + 0.176091259055681 ); We want k to be too
         * large rather than too small. The error in the first-order Taylor
         * series approximation is in our favor, so we just round up the constant
         * enough to compensate for any error in the multiplication of (i - Bias)
         * by 0.301029995663981; since |i - Bias| <= 1077, and 1077 * 0.30103 *
         * 2^-52 ~=~ 7.2e-14, adding 1e-13 to the constant term more than
         * suffices. Hence we adjust the constant term to 0.1760912590558. (We
         * could get a more accurate k by invoking log10, but this is probably
         * not worthwhile.) */
  
        i -= Bias;
        denorm = 0;
      }
    else
      {
        /* d is denormalized */
  
        i = bbits + be + (Bias + (P - 1) - 1);
        x = i > 32 ? word0(d) << (64 - i) | word1(d) >> (i - 32)
          : word1(d) << (32 - i);
        d2 = x;
        word0(d2) -= 31 * Exp_msk1;       /* adjust exponent */
        i -= (Bias + (P - 1) - 1) + 1;
        denorm = 1;
      }
  
    ds = (d2 - 1.5) * 0.289529654602168 + 0.1760912590558 + i * 0.301029995663981;
    k = (int)ds;
    if (ds < 0. && ds != k)
      {
        k--;  /* want k = floor(ds) */
      }
  
    k_check = 1;
  
    if (k >= 0 && k <= Ten_pmax)
      {
        if (d < tens[k])
          k--;
        k_check = 0;
      }
  
    j = bbits - i - 1;
    if (j >= 0)
      {
        b2 = 0;
        s2 = j;
      }
    else
      {
        b2 = -j;
        s2 = 0;
      }
  
    if (k >= 0)
      {
        b5 = 0;
        s5 = k;
        s2 += k;
      }
    else
      {
        b2 -= k;
        b5 = -k;
        s5 = 0;
      }
  
    if (mode < 0 || mode > 9)
      {
        mode = 0;
      }
  
    try_quick = 1;
    if (mode > 5)
      {
        mode -= 4;
        try_quick = 0;
      }
  
    leftright = 1;
    switch (mode)
      {
      case 0:
      case 1:
        ilim = ilim1 = -1;
        i = 18;
        ndigits = 0;
        break;
  
      case 2:
        leftright = 0;
        /* FALLTHROUGH */
      case 4:
        if (ndigits <= 0)
          {
            ndigits = 1;
          }
  
        ilim = ilim1 = i = ndigits;
        break;
  
      case 3:
        leftright = 0;
        /* FALLTHROUGH */
      case 5:
        i = ndigits + k + 1;
        ilim = i;
        ilim1 = i - 1;
        if (i <= 0)
          {
            i = 1;
          }
      }
  
    j = sizeof(unsigned long);
    for (result_k = 0;
         (signed)(sizeof(Bigint) - sizeof(unsigned long) + j) <= i;
         j <<= 1)
      {
        result_k++;
      }
  
    result = Balloc(result_k);
    s = s0 = (char *)result;
  
    if (ilim >= 0 && ilim <= Quick_max && try_quick)
      {
        /* Try to get by with floating-point arithmetic. */
  
        i = 0;
        d2 = d;
        k0 = k;
        ilim0 = ilim;
        ieps = 2;                 /* conservative */
  
        if (k > 0)
          {
            ds = tens[k & 0xf];
            j = k >> 4;
  
            if (j & Bletch)
              {
                /* Prevent overflows */
  
                j &= Bletch - 1;
                d /= bigtens[n_bigtens - 1];
                ieps++;
              }
  
            for (; j; j >>= 1, i++)
              {
                if (j & 1)
                  {
                    ieps++;
                    ds *= bigtens[i];
                  }
              }
  
            d /= ds;
          }
        else if ((j_1 = -k))
          {
            d *= tens[j_1 & 0xf];
            for (j = j_1 >> 4; j; j >>= 1, i++)
              {
                if (j & 1)
                  {
                    ieps++;
                    d *= bigtens[i];
                  }
              }
          }
  
        if (k_check && d < 1. && ilim > 0)
          {
            if (ilim1 <= 0)
              {
                goto fast_failed;
              }
  
            ilim = ilim1;
            k--;
            d *= 10.;
            ieps++;
          }
  
        eps = ieps * d + 7.;
        word0(eps) -= (P - 1) * Exp_msk1;
        if (ilim == 0)
          {
            S = mhi = 0;
            d -= 5.;
            if (d > eps)
              goto one_digit;
  
            if (d < -eps)
              goto no_digits;
  
            goto fast_failed;
          }
  
  #ifndef No_leftright
        if (leftright)
          {
            /* Use Steele & White method of only generating digits needed. */
  
            eps = 0.5 / tens[ilim - 1] - eps;
            for (i = 0; ; )
              {
                L = (int)d;
                d -= L;
                *s++ = '0' + (int)L;
                if (d < eps)
                  {
                    goto ret1;
                  }
  
                if (1. - d < eps)
                  {
                    goto bump_up;
                  }
  
                if (++i >= ilim)
                  {
                    break;
                  }
  
                eps *= 10.;
                d *= 10.;
              }
          }
        else
          {
  #endif
            /* Generate ilim digits, then fix them up. */
  
            eps *= tens[ilim - 1];
            for (i = 1; ; i++, d *= 10.)
              {
                L = (int)d;
                d -= L;
                *s++ = '0' + (int)L;
                if (i == ilim)
                  {
                    if (d > 0.5 + eps)
                      {
                        goto bump_up;
                      }
                    else if (d < 0.5 - eps)
                      {
                        while (*--s == '0');
                        s++;
                        goto ret1;
                      }
  
                    break;
                  }
              }
  #ifndef No_leftright
          }
  #endif
  
      fast_failed:
        s = s0;
        d = d2;
        k = k0;
        ilim = ilim0;
      }
  
    /* Do we have a "small" integer? */
  
    if (be >= 0 && k <= Int_max)
      {
        /* Yes. */
  
        ds = tens[k];
        if (ndigits < 0 && ilim <= 0)
          {
            S = mhi = 0;
            if (ilim < 0 || d <= 5 * ds)
              {
                goto no_digits;
              }
  
            goto one_digit;
          }
  
        for (i = 1; ; i++)
          {
            L = (int)(d / ds);
            d -= L * ds;
  
  #ifdef Check_FLT_ROUNDS
            /* If FLT_ROUNDS == 2, L will usually be high by 1 */
  
            if (d < 0)
              {
                L--;
                d += ds;
              }
  #endif
            *s++ = '0' + (int)L;
            if (i == ilim)
              {
                d += d;
                if (d > ds || (d == ds && (L & 1)))
                  {
                  bump_up:
                    while (*--s == '9')
                      if (s == s0)
                        {
                          k++;
                          *s = '0';
                          break;
                        }
  
                    ++*s++;
                  }
  
                break;
              }
  
            if (!(d *= 10.))
              {
                break;
              }
          }
  
        goto ret1;
      }
  
    m2 = b2;
    m5 = b5;
    mhi = mlo = 0;
    if (leftright)
      {
        if (mode < 2)
          {
            i = denorm ? be + (Bias + (P - 1) - 1 + 1) : 1 + P - bbits;
          }
        else
          {
            j = ilim - 1;
            if (m5 >= j)
              m5 -= j;
            else
              {
                s5 += j -= m5;
                b5 += j;
                m5 = 0;
              }
  
            if ((i = ilim) < 0)
              {
                m2 -= i;
                i = 0;
              }
          }
  
        b2 += i;
        s2 += i;
        mhi = i2b(1);
      }
  
    if (m2 > 0 && s2 > 0)
      {
        i = m2 < s2 ? m2 : s2;
        b2 -= i;
        m2 -= i;
        s2 -= i;
      }
  
    if (b5 > 0)
      {
        if (leftright)
          {
            if (m5 > 0)
              {
                mhi = pow5mult(mhi, m5);
                b1 = mult(mhi, b);
                Bfree(b);
                b = b1;
              }
  
            if ((j = b5 - m5))
              {
                b = pow5mult(b, j);
              }
          }
        else
          {
            b = pow5mult(b, b5);
          }
      }
  
    S = i2b(1);
    if (s5 > 0)
      {
        S = pow5mult(S, s5);
      }
  
    /* Check for special case that d is a normalized power of 2. */
  
    if (mode < 2)
      {
        if (!word1(d) && !(word0(d) & Bndry_mask) && word0(d) & Exp_mask)
          {
            /* The special case */
  
            b2 += Log2P;
            s2 += Log2P;
            spec_case = 1;
          }
        else
          {
            spec_case = 0;
          }
      }
  
    /* Arrange for convenient computation of quotients: shift left if
     * necessary so divisor has 4 leading 0 bits.
     *
     * Perhaps we should just compute leading 28 bits of S once and for all
     * and pass them and a shift to quorem, so it can do shifts and ors
     * to compute the numerator for q.
     */
  
  #ifdef Pack_32
    if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds - 1]) : 1) + s2) & 0x1f))
      {
        i = 32 - i;
      }
  #else
    if ((i = ((s5 ? 32 - hi0bits(S->x[S->wds - 1]) : 1) + s2) & 0xf))
      {
        i = 16 - i;
      }
  #endif
  
    if (i > 4)
      {
        i -= 4;
        b2 += i;
        m2 += i;
        s2 += i;
      }
    else if (i < 4)
      {
        i += 28;
        b2 += i;
        m2 += i;
        s2 += i;
      }
  
    if (b2 > 0)
      {
        b = lshift(b, b2);
      }
  
    if (s2 > 0)
      {
        S = lshift(S, s2);
      }
  
    if (k_check)
      {
        if (cmp(b, S) < 0)
          {
            k--;
            b = multadd(b, 10, 0);        /* we botched the k estimate */
            if (leftright)
              {
                mhi = multadd(mhi, 10, 0);
              }
  
            ilim = ilim1;
          }
      }
  
    if (ilim <= 0 && mode > 2)
      {
        if (ilim < 0 || cmp(b, S = multadd(S, 5, 0)) <= 0)
          {
            /* no digits, fcvt style */
  
          no_digits:
            k = -1 - ndigits;
            goto ret;
          }
  
      one_digit:
        *s++ = '1';
        k++;
        goto ret;
      }
  
    if (leftright)
      {
        if (m2 > 0)
          {
            mhi = lshift(mhi, m2);
          }
  
        /* Compute mlo -- check for special case that d is a normalized power of
         * 2. */
  
        mlo = mhi;
        if (spec_case)
          {
            mhi = Balloc(mhi->k);
            Bcopy(mhi, mlo);
            mhi = lshift(mhi, Log2P);
          }
  
        for (i = 1; ; i++)
          {
            dig = quorem(b, S) + '0';
            /* Do we yet have the shortest decimal string that will round to d? */
            j = cmp(b, mlo);
            delta = diff(S, mhi);
            j_1 = delta->sign ? 1 : cmp(b, delta);
            Bfree(delta);
  #ifndef ROUND_BIASED
            if (j_1 == 0 && !mode && !(word1(d) & 1))
              {
                if (dig == '9')
                  {
                   goto round_9_up;
                  }
  
                if (j > 0)
                  {
                    dig++;
                  }
  
                *s++ = dig;
                goto ret;
              }
  #endif
            if (j < 0 || (j == 0 && !mode
  #ifndef ROUND_BIASED
                          && (!(word1(d) & 1))
  #endif
              ))
              {
                if ((j_1 > 0))
                  {
                    b = lshift(b, 1);
                    j_1 = cmp(b, S);
                    if ((j_1 > 0 || (j_1 == 0 && (dig & 1))) && dig++ == '9')
                      {
                        goto round_9_up;
                      }
                  }
  
                *s++ = dig;
                goto ret;
              }
  
            if (j_1 > 0)
              {
                if (dig == '9')
                  {
                    /* possible if i == 1 */
  
                    round_9_up:
                    *s++ = '9';
                    goto roundoff;
                  }
  
                *s++ = dig + 1;
                goto ret;
              }
  
            *s++ = dig;
            if (i == ilim)
              {
                break;
              }
  
            b = multadd(b, 10, 0);
            if (mlo == mhi)
              {
                mlo = mhi = multadd(mhi, 10, 0);
              }
            else
              {
                mlo = multadd(mlo, 10, 0);
                mhi = multadd(mhi, 10, 0);
              }
          }
      }
    else
      {
        for (i = 1; ; i++)
          {
            *s++ = dig = quorem(b, S) + '0';
            if (i >= ilim)
              {
                break;
              }
  
            b = multadd(b, 10, 0);
          }
      }
  
    /* Round off last digit */
  
    b = lshift(b, 1);
    j = cmp(b, S);
    if (j > 0 || (j == 0 && (dig & 1)))
      {
      roundoff:
        while (*--s == '9')
          if (s == s0)
            {
              k++;
              *s++ = '1';
              goto ret;
            }
  
        ++*s++;
      }
    else
      {
        while (*--s == '0');
        s++;
      }
  
  ret:
    Bfree(S);
    if (mhi)
      {
        if (mlo && mlo != mhi)
          {
            Bfree(mlo);
          }
  
        Bfree(mhi);
      }
  ret1:
    Bfree(b);
    if (s == s0)
      {
        /* Don't return empty string */
  
        *s++ = '0';
        k = 0;
      }
  
    *s = 0;
    *decpt = k + 1;
    if (rve)
      {
        *rve = s;
      }
  
    return s0;
  }
  